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A207621 Triangle of coefficients of polynomials v(n,x) jointly generated with A207620; see the Formula section.

%I A207621 #9 Mar 31 2023 03:22:53
%S A207621 1,2,2,3,6,2,4,13,10,2,5,24,31,14,2,6,40,76,57,18,2,7,62,161,176,91,
%T A207621 22,2,8,91,308,456,340,133,26,2,9,128,546,1044,1045,584,183,30,2,10,
%U A207621 174,912,2178,2794,2080,924,241,34,2,11,230,1452,4224,6721,6370
%N A207621 Triangle of coefficients of polynomials v(n,x) jointly generated with A207620; see the Formula section.
%F A207621 u(n,x)=u(n-1,x)+v(n-1,x), v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1.
%e A207621 First five rows:
%e A207621 1
%e A207621 2...2
%e A207621 3...6...2
%e A207621 4...13...10...2
%e A207621 5...24...31...14...2
%t A207621 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A207621 u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t A207621 v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1
%t A207621 Table[Factor[u[n, x]], {n, 1, z}]
%t A207621 Table[Factor[v[n, x]], {n, 1, z}]
%t A207621 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A207621 TableForm[cu]
%t A207621 Flatten[%]    (* A207620 *)
%t A207621 Table[Expand[v[n, x]], {n, 1, z}]
%t A207621 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A207621 TableForm[cv]
%t A207621 Flatten[%]    (* A207621 *)
%Y A207621 Cf. A207620.
%K A207621 nonn,tabl
%O A207621 1,2
%A A207621 _Clark Kimberling_, Feb 20 2012